Active Convolved Illumination with Deep Transfer Learning for Complex Beam Transmission through Atmospheric Turbulence

Atmospheric turbulence imposes a fundamental limitation across a broad range of applications, including optical imaging, remote sensing, and free-space optical communication. Recent advances in adaptive optics, wavefront shaping, and machine learning, driven by synergistic progress in fundamental theories, optoelectronic hardware, and computational algorithms, have demonstrated substantial potential in mitigating turbulence-induced distortions. Recently, active convolved illumination (ACI) was proposed as a versatile and physics-driven technique for transmitting structured light beams with minimal distortion through highly challenging turbulent regimes. While distinct in its formulation, ACI shares conceptual similarities with other physics-driven distortion correction approaches and stands to benefit from complementary integration with data-driven deep learning (DL) models. Inspired by recent work coupling deep learning with traditional turbulence mitigation strategies, the present work investigates the feasibility of integrating ACI with neural network-based methods. We outline a conceptual framework for coupling ACI with data-driven models and identify conditions under which learned representations can meaningfully support ACI's correlation-injection mechanism. As a representative example, we employ a convolutional neural network (CNN) together with a transfer-learning approach to examine how a learned model may operate in tandem with ACI. This exploratory study demonstrates feasible implementation pathways and establishes an early foundation for assessing the potential of future ACI-DL hybrid architectures, representing a step toward evaluating broader synergistic interactions between ACI and modern DL models.